# PUBLIC SCHOOLS OF EDISON TOWNSHIP OFFICE OF CURRICULUM AND INSTRUCTION GEOMETRY HONORS. Middle School and High School

Save this PDF as:

Size: px
Start display at page:

Download "PUBLIC SCHOOLS OF EDISON TOWNSHIP OFFICE OF CURRICULUM AND INSTRUCTION GEOMETRY HONORS. Middle School and High School"

## Transcription

1 PUBLIC SCHOOLS OF EDISON TOWNSHIP OFFICE OF CURRICULUM AND INSTRUCTION GEOMETRY HONORS Length of Course: Elective/Required: Schools: Term Required Middle School and High School Eligibility: Grades 8-12 Credit Value: (High School Only) 5 Credits Date Approved: August 25, 2014

2 GEOMETRY HONORS TABLE OF CONTENTS Statement of Purpose 3 Course Objectives 4 Suggested Time Line (Level: Honors) 7 Unit 0: Chapter 0 Preparing for Geometry 8 Unit 1: Chapter 1 - Tools of Geometry 10 Unit 2: Chapter 2 - Reasoning and Proof 12 Unit 3: Chapter 3 - Parallel and Perpendicular Lines 15 Unit 4: Chapter 4 - Congruent Triangles 17 Unit 5: Chapter 5 - Relationships in Triangles 20 Unit 6: Chapter 6 Quadrilaterals 22 Unit 7: Chapter 7 - Proportions and Similarity 24 Unit 8: Chapter 8 - Right Triangles/ Trigonometry 26 Unit 9: Chapter 9 - Transformations and Symmetry 28 Unit 10: Chapter 10 Circles 31 Unit 11: Chapter 11 Area of Polygons and Circles 34 Unit 12: Chapter 12 Extending Surface Area/ Volume 36 Unit 13: Chapter 13 Probability and Measurement 38

3 GEOMETRY HONORS 3 Statement of Purpose This course of study has been designed for the Geometry Honors course. The curriculum introduces geometric topics, skills, and concepts. The material should be connected to real-world situations as often as possible, as suggested in the curriculum. This course curriculum guide provides a thorough preparation for geometric questions that may be included on the state assessment. In order to promote the effective implementation of this program, the following suggestions are provided: 1. Formative assessment should be used throughout this course, as with any math course, in order to monitor students learning and instruction such be adjusted as needed. 2. Instruction should be differentiated in order to accommodate the different ways students learn. 3. Students should be encouraged to maintain an organized and thorough set of notes in a notebook. Teachers should indicate the expected format and content and should explain how notebooks can be effectively utilized. 4. Meaningful and relevant homework assignments should be given to students on a regular basis to encourage practice of new skills and concepts. 5. Examples of application of mathematics and specifically Algebra in careers and everyday-life situations should be provided as motivation wherever possible. 6. Students should be required to use correct mathematical terminology at all times. 7. The use of technology is encouraged wherever possible in order to foster the impact on students learning and understanding. 8. Modifications and accommodations should be included where necessary to meet student s Individual Education Plans (IEP).

4 GEOMETRY HONORS 4 The student will be able to: Chapter 1 Course Objectives Develop an awareness of the structure of a mathematical system, connecting definitions, postulates, logical reasoning, and theorems. Use construction to explore attributes of geometric figures and to make conjectures about geometric relationships. Use one- and two-dimensional coordinate systems to represent points, lines, rays, line segments, and figures. Find areas of regular polygons, circles, and composite figures. Chapter 2 Use inductive reasoning to formulate a conjecture. Use logical reasoning to prove statements are true and find counterexamples to disprove statements that are false. Determine the validity of a conditional statement, its converse, inverse, and contrapostive. Use deductive reasoning to prove a statement. Chapter 3 Make conjectures about lines and determine the validity of the conjectures. Make conjectures about angles and determine the validity of the conjectures. Use slopes of equations of lines to investigate geometric relationships, including parallel lines and perpendicular lines. Use one- and two-dimensional coordinate systems to represent lines. Chapter 4 Make conjectures about polygons. Use numeric and geometric patterns to make generalizations about geometric properties. Use logical reasoning to prove statements are true. Chapter 5 Use slope and equations of lines to investigate geometric relationships, including special segments of triangles. Recognize and know historical development of geometric systems and know that mathematics was developed for a variety of purposes. Analyze geometric relationships in order to verify conjectures.

5 GEOMETRY HONORS 5 Chapter 6 Use geometric concepts and properties to solve problems in fields such as art and architecture. Identify and apply mathematics to everyday experience, to activities in and outside of school, with other disciplines, and with other mathematical topics. Communicate mathematical ideas using language, efficient tools, appropriate units, and graphical, numerical, physical, or algebraic mathematical models. Chapter 7 Use ratios to solve problems involving similar figures. Formulate and test conjectures about the properties and attributes of polygons and their component parts based on explorations and concrete models. Chapter 8 Use and extend similarity properties to explore and justify conjectures about geometric figures. Derive, extend, and use the Pythagorean Theorem. Identify and apply patterns from right triangles to solve meaningful problems, including special right triangles ( and ) and triangles with sides that are Pythagorean triples. Develop, apply, and justify triangle similarity relationships, such as trigonometric ratios using a variety of methods. Chapter 9 Use congruence transformations to make conjectures and justify properties of geometric figures. Chapter 10 Find areas of sectors and arc lengths of circles using proportional reasoning. Use numeric and geometric patterns to make generalizations about geometric properties including properties of angle relationships in circles. Chapter 11 Find areas of regular polygons, circles, and composite figures. Find areas of sectors and arc lengths of circles using proportional reasoning.

6 GEOMETRY HONORS 6 Chapter 12 Find surface areas and volumes of prisms, pyramids, spheres, cones, cylinders, and composites of these figures. Describe the effect on area and volume when one or more dimensions of a figure are changed. Chapter 13 Understand sample spaces and design simulations Compute probabilities for independent, dependent, mutually exclusive, not mutually exclusive, and conditional events. Calculate geometric probabilities. Note - All objectives will include applications to real-life situations. For Common Core Standards in full visit Standards can be implemented in addition to the standards listed in this curriculum.

7 GEOMETRY HONORS 7 Suggested Time Line (Level: Honors) UNIT # of PERIODS COMPLETE FOR EYA Unit 0: Chapter 0 Preparing for Geometry Optional 5 Unit 1: Chapter 1 - Tools of Geometry , 1.7 Unit 2: Chapter 2 - Reasoning and Proof 12 Unit 3: Chapter 3 - Parallel and Perpendicular Lines Unit 4: Chapter 4 - Congruent Triangles 18 (end MP 1) 4.1, Unit 5: Chapter 5 - Relationships in Triangles Unit 6: Chapter 6 - Quadrilaterals Unit 7: Chapter 7 - Proportions and Similarity 14 (end MP 2) Unit 8: Chapter 8 - Right Triangles/ Trigonometry , 8.7 Unit 9: Chapter 9 - Transformations and Symmetry Unit 10: Chapter 10 - Circles 14 (end MP 3) , 10.8 Unit 11: Chapter 11 Area of Polygons and Circles , 11.3 Unit 12: Chapter 12 Extending Surface Area/ Volume , 12.4, 12.5, 12.6 Unit 13: Chapter 13 Probability and Measurement 10 (end MP 4) Note - The above suggested time line is a rough guideline based on suggestions from the Glencoe Geometry textbook. Teachers must adjust their timing and pacing as they feel necessary to accommodate actual class periods available.

8 GEOMETRY HONORS 8 Targeted Standards: Unit Title: Chapter 0 Preparing For Geometry Unit Objectives/Conceptual Understandings: The concepts presented in Chapter 0 are review from previous courses. You may wish to use all or some of the chapter at the beginning of the school year to refresh students' skills. Or you may wish to begin with Chapter 1 and use the Chapter 0 lessons as needed to reinforce prerequisite skills as you progress through the program. Unit : Teacher-generated assessments will be used. Progress Indicators CC.9-12.S.CP.1 Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) CC.9-12.A.CED.4* Students extend their work with algebraic properties and solving equations in one variable to solving literal equations for a given variable. CC.9-12.A.REI.3 CC.9-12.A.CED.1* Students have written and solved linear equations in one variable. Now they extend this work to inequalities. The methods for solving inequalities are very similar to the methods for solving equations; many students strengthen their understanding by studying both. As with equations, students will create and use inequalities to solve Unit vocabulary including: a. experiment b. trial c. outcome d. event e. probability f. theoretical probability g. experimental probability h. ordered pair i. x-coordinate j. y-coordinate k. quadrant l. origin m. system of equations n. substitution o. elimination p. Product Property q. Quotient Property Convert units of measure within the customary and metric systems. Convert units of measure between the customary and metric systems. Find the probability of simple events. Use the order of operations to evaluate algebraic expressions. Use algebra to solve linear equations. Use algebra to solve linear inequalities. Name and graph points in Use pretest and posttest provided in the text

9 GEOMETRY HONORS 9 Unit Title: Chapter 0 Preparing For Geometry (cont.) Progress Indicators problems in contextual situations. the coordinate plane. CC.9-12.A.CED.2* CC.9-12.A.REI.6 Students have seen that the relationship between two or more variables can be represented as an equation or inequality and as a graph. Understanding equivalent representations and fluently translating between them are important for solving problems. For example, the connection between an equation and its graph is key to understanding how to use a graph to solve a system of equations. Use graphing, substitution, and elimination to solve systems of linear equations. Evaluate square roots and simplify radical expressions. Resources: Essential Materials, Supplementary Materials, Links to Best Practices, Leveled Worksheets, Personal Tutor, Virtual Manipulatives, 5-Minute Checks, Graphing Calculator Instructional Adjustments: Leveled Worksheets, Differentiation Resources, Scaffolding Questions

10 GEOMETRY HONORS 10 Unit Title: Chapter 1 Tools of Geometry Targeted Standards: G.CO Experiment with transformations in the plane. G.GMD Explain volume formulas and use them to solve problems. G.MG Apply geometric concepts in modeling situations. G.GPE Translate between the geometric description and the equation for a conic section. Unit Objectives/Conceptual Understandings: Students will be able to: Develop an awareness of the structure of a mathematical system, connecting definitions, postulates, logical reasoning and theorems. Use construction to explore attributes of geometric figures to make conjectures about geometric relationships. Use one and two dimensional coordinate systems to represent points, lines, rays, line segments, and figures. Find areas of regular polygons, circles, and composite figures. Essential Questions: Why do we measure? Unit : Teacher-generated assessments will be used. G.CO.1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc. G.CO.12 Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). G.MG.1 Use geometric Unit vocabulary including: a. collinear b. coplanar c. congruent d. midpoint e. segment bisector f. angle g. vertex h. angle bisector i. perpendicular j. polygon k. perimeter l. volume Identify and model points, lines, and planes. Identify intersecting lines and planes. Identify and model points, lines, and planes. Identify intersecting lines and planes. Measure segments. Calculate with measures. Find the distance between two points. Find the midpoint of a segment. Challenge students to develop three-dimensional models to demonstrate difficult geometric concepts related to points, lines, and planes. Some examples include: Develop a model to show that three points can be noncollinear. Develop a demonstration to show that three points are coplanar, but four points can be noncoplanar. Develop a threedimensional model of lines that are not Use formative assessments suggested in the textbook. Use Guided Practice, Check Your Understanding, HOT problems, and Spiral Reviews as needed. Use Ticket Out the Door Section 1.2 and 1.6. Use Mid-Chapter

11 GEOMETRY HONORS 11 Unit Title: Chapter 1 Tools of Geometry (cont.) shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder). G.GPE.7 Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula. G.GMD.3 Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems. Visualize relationships between two-dimensional and three-dimensional objects. Measure segments. Calculate with measures. Find the distance between two points. Find the midpoint of a segment. Measure and classify angles. Identify and use congruent angles and the bisector of an angle. Identify and use special pairs of angles. Identify perpendicular lines. Identify and name polygons. Find perimeter or circumference and area of two-dimensional figures. Identify and name threedimensional figures. Find surface area and volume. Measure and classify angles. Identify and use congruent angles and the bisector of an angle. Identify and use special pairs of angles. Identify perpendicular lines. Identify and name polygons. Find perimeter, circumference, and area of two-dimensional figures. Identify and name threedimensional figures. Find surface area and volume. Resources: Leveled Worksheets, Personal Tutor, Virtual Manipulatives, 5-Minute Checks found on connect.ed.mcgraw-hill.com Geometer Sketchpad Graphing Calculator Teaching Geometry with Manipulatives parallel and do not intersect. Have students sketch three different segments that each have (0, 0) as a midpoint. Write the coordinates of the endpoints of each segment. What do you notice about the coordinates? Have students list each angle relationship presented in the Key Concept boxes of this lesson on pages Then, have students write one or two sentences to describe each relationship and provide an example. When discussing surface area, provide students with the opportunity to make nets, cut them out, and then put them together to make a solid. This should help them better understand surface area. Instructional Adjustments: Quiz Lesson p 45. Use Self-Check Quizzes as needed. Use Leveled Worksheets. Use Lesson Resources to provide differentiation. Use scaffolding questions provided at the start of each lesson. Use error analysis and Watch Out tips suggested in the textbook. Use Tip for New Teachers suggested in the textbook.

12 GEOMETRY HONORS 12 Unit Title: Chapter 2 Reasoning and Proof Targeted Standards: G.CO Prove geometric theorems. G.MG Apply geometric concepts in modeling situations. Unit Objectives/Conceptual Understandings: Students will be able to: Use inductive reasoning to formulate a conjecture. Use logical reasoning to prove statements are true and find counterexamples to disprove statements that are false. Determine the validity of a conditional statement, its converse, inverse, and contrapostive. Use deductive reasoning to prove a statement. Essential Questions: Why is it important to be able to think logically? Unit : Teacher-generated assessments will be used. G.CO.9 Prove theorems about lines and angles. G.CO.12 Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). G.MG.3 Apply geometric methods to solve problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios). Unit vocabulary including: a. inductive reasoning b. conjecture c. counterexample d. negation e. if-then statement f. hypothesis g. conclusion h. converse i. inverse j. postulate k. proof l. theorem Use logic to find counterexamples and use inductive reasoning to formulate a conjecture. Make conjectures based on inductive reasoning. Find counterexamples. Determine truth values of negations, conjunctions, and disjunctions and represent them using Venn diagrams. Analyze statements in if-then form. Write converses, inverses, and contrapositives. Use the Law of Detachment. Organize students into small groups. Each student should come up with at least two statements that are not always true and the other students in the group should find the counterexamples. If students have difficulty understanding the truth value of conditional statements, then have students determine what type of conditional statements are never true. Have them analyze truth tables for conditional statements and find concrete examples where the hypothesis is always true and the conclusion is always false. Use formative assessments suggested in the textbook. Use Guided Practice, Check Your Understanding, HOT problems, and Spiral Reviews as needed. Use Ticket Out the Door Section 2.1 and 2.8. Use Mid-Chapter Quiz Lesson p 135.

13 GEOMETRY HONORS 13 Unit Title: Chapter 2 Reasoning and Proof (cont.) Develop an awareness of a mathematical system, connecting definitions, postulates, and logical reasoning. Use logical reasoning to prove statements are true. Use the Law of Syllogism. Identify and use basic postulates about points, lines, and planes. Write paragraph proofs. Provide students with algebraic and geometric proofs that are missing the justifications for each step. At least one proof should contain errors. Have students fill in the justifications and explain the errors. Use Self-Check quizzes as needed. Analyze statements in ifthen form. Write the converse, inverse, and contrapositive of if-then statements. Learn to use the Law of Detachment and the Law of Syllogism. Use deductive reasoning to prove a statement. Construct and justify statements about geometric figures, using basic postulates and paragraph proofs. Use algebra to write twocolumn proofs. Use properties of equality to write geometric proofs. Write proofs involving segment addition. Write proofs involving congruence. Write proofs involving supplementary and complementary angles. Use algebra to write twocolumn proofs and use the properties of equality to write geometric proofs. Write proofs involving congruent and right angles. Write proofs involving segment addition and segment congruence.

14 GEOMETRY HONORS 14 Unit Title: Chapter 2 Reasoning and Proof (cont.) Write proofs involving supplementary and complementary angles. Write proofs involving congruent and right angles. Use deductive reasoning to prove a statement. Resources: Leveled Worksheets, Personal Tutor, Virtual Manipulatives, 5-Minute Checks found on connect.ed.mcgraw-hill.com Geometer Sketchpad Graphing Calculator Teaching Geometry with Manipulatives Instructional Adjustments: Use Leveled Worksheets. Use Lesson Resources to provide differentiation. Use scaffolding questions provided at the start of each lesson. Use error analysis and Watch Out tips suggested in the textbook. Use Tip for New Teachers suggested in the textbook.

15 GEOMETRY HONORS 15 Unit Title: Chapter 3 Parallel and Perpendicular Lines Targeted Standards: G.CO Experiment with transformations in the plane. G.MG Apply geometric concepts in modeling situations. G.GPE Translate between the geometric description and the equation for a conic section. Unit Objectives/Conceptual Understandings: Students will be able to: Make conjectures about lines and determine the validity of the conjectures. Use construction to explore attributes of geometric figures to make conjectures about geometric relationships. Make conjectures about angles and determine the validity of the conjectures. Find areas of regular polygons, circles, and composite figures. Use slopes of equations of lines to investigate geometric relationships, including parallel lines and perpendicular lines. Use one- and two-dimensional coordinate systems to represent lines. Essential Questions: Why do we have undefined terms such as point and line? How can we use undefined terms? Unit : Teacher-generated assessments will be used. Progress Indicators G.CO.1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc. G.CO.9 Prove theorems about lines and angles. G.CO.12 Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Unit vocabulary including: a. parallel lines b. skew lines c. parallel planes d. transversal e. interior angles f. exterior angles g. corresponding angle h. slope i. rate of change j. slope-intercept form k. point-slope form l. equidistant Identify relationships between two lines or two planes. Name angle pairs formed by parallel lines and Identify the relationship between two lines or two planes. Name angle pairs formed by parallel lines and transversals. Identify the relationships between two lines or planes. Name angle pairs formed by parallel lines and transversals. Use properties of parallel lines to determine congruent angles. Graph and write equations of lines given characteristics Use masking tape to mark two parallel lines and a transversal on the floor. Have pairs of students stand in angles that are congruent or supplementary, and have them explain whether their angles are alternate interior, alternate exterior, corresponding, or consecutive interior angles. Have students graph y = x 2 on a coordinate plane. They can use a graphing calculator to generate the graph. Explain that a tangent line intersects the graph in one place. Have them predict where the tangent line of Use formative assessments suggested in the textbook. Use Guided Practice, Check Your Understanding, HOT problems, and Spiral Reviews as needed. Use Ticket Out the Door Section 3.1 and 3.5. Use Mid-Chapter Quiz Lesson p 197.

16 GEOMETRY HONORS 16 Progress Indicators G.MG.3 Apply geometric methods to solve problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios). G.GPE.5 Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). Unit Title: Chapter 3 Parallel and Perpendicular Lines (cont.) transversals. Use theorems to determine the relationships between specific pairs of angles. Use algebra to find angle measurements. Find slopes of lines. Use slope to identify parallel and perpendicular lines. Write an equation of a line given information about the graph. Solve problems by writing equations. Recognize the angle relationships that occur when parallel lines are cut by a transversal. such as two points, a point and a slope, or a slope and y- intercept. Recognize the angle relationships that occur when parallel lines are cut by a transversal. Use angle relationships to prove that lines are parallel. Use angle relationships to prove that two lines are parallel. Use angle relationships to prove that lines are parallel. Find the distance between a point and a line. Find the distance between two parallel lines. Resources: Leveled Worksheets, Personal Tutor, Virtual Manipulatives, 5-Minute Checks found on connect.ed.mcgraw-hill.com Geometer Sketchpad Graphing Calculator Teaching Geometry with Manipulatives their function will be located. Have them sketch the line and predict the slope of the line. Explain to students that they will learn more about tangent lines to functions as they begin their study of calculus. Instruct students to draw two lines cut by a transversal with given specific angle measure criteria. The students may work together in small groups of 3 or 4 to discuss whether the lines must be parallel. Facilitate the discussions so that students discern that more angle measures can be found with certainty when the lines are parallel than when the lines are not parallel. Instructional Adjustments: Use Self-Check Quizzes as needed. Use Leveled Worksheets. Use Lesson Resources to provide differentiation. Use scaffolding questions provided at the start of each lesson. Use error analysis and Watch Out tips suggested in the textbook. Use Tip for New Teachers suggested in the textbook.

17 GEOMETRY HONORS 17 Unit Title: Chapter 4 Congruent Triangles Targeted Standards: G.CO Experiment with transformations in the plane. G.SRT Understand similarity in terms of similarity transformations G.GPE Translate between the geometric description and the equation for a conic section. Unit Objectives/Conceptual Understandings: Make conjectures about polygons. Use numeric and geometric patterns to make generalizations about geometric properties. Use logical reasoning to prove statements are true. Essential Questions: How can you compare two objects? How can you tell if two objects are congruent? How can you tell if two triangles are congruent? Unit : Teacher-generated assessments will be used. G.CO.5 Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another. G.CO.6 Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are Unit vocabulary including: a. equiangular triangle b. equilateral triangle c. isosceles triangle d. scalene triangle e. auxiliary line f. congruent g. congruent polygons h. corresponding parts i. included angle j. included side k. base angle l. transformation m. preimage n. image o. reflection Identify and classify triangles by angle measures and side measures. Apply the Triangle Angle-Sum Theorem and the Exterior Angle Theorem. Name and use corresponding parts of congruent triangles. Prove triangles congruent using the definition of congruence Interpersonal Students work in groups of 2 or 3 to explore the triangle classifications. Ask students to explore and discuss questions such as these: Can you draw an equiangular triangle with a 90 angle? Can you draw a right triangle that has an obtuse angle? Facilitate the discussions so that students discover which triangle classifications are mutually exclusive and which are not Suggested quiz after section 4.4 Exit tickets provided in text Teacher-generated exit tickets Suggested quiz after section 4.6 Teacher-generated formative/summative assessment

18 GEOMETRY HONORS 18 Unit Title: Chapter 4 Congruent Triangles (cont.) congruent. G.CO.7 Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent. G.CO.10 Prove theorems about triangles. G.CO.12 Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). G.SRT.5 Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures. G.GPE.4 Use coordinates to prove simple geometric theorems algebraically. p. translation q. rotation Triangle Angle Sum Theorem Properties of Triangle Congruence Triangle Congruence Postulates: SSS, SAS, ASA, AAS, HL Isosceles Triangle Theorem Coordinate Proof Use the SSS and SAS Postulates to test for triangle congruence. Use the ASA and AAS Postulates to test for triangle congruence. Use properties of isosceles and equilateral triangles. Identify reflections, translations, and rotations. Verify congruence after a congruence transformation. Position and label triangles for use in coordinate proofs. Write coordinate proofs. Multiple Representations In Exercise 45, students investigate the sum of the measures of the exterior angles of a triangle using geometric sketches, a table, a verbal description, and a paragraph proof. Extension Have students draw ΔABC with vertices A( 8, 8), B( 2, 5), and C( 8, 2). Next, have students draw ΔPTS with vertices P(8, 8), T(2, 5), and S(8, 2). Ask students how they can verify that the corresponding sides of the triangles are congruent. Further, facilitate discussion about whether the corresponding angles of ΔABC and ΔPTS are congruent. Students can use the distance formula to prove that corresponding sides are congruent. Further discussion about the angles may include suggestions that the triangles are exactly the same because one is a reflection of the other, or that the equal side lengths require equal angles.

19 GEOMETRY HONORS 19 Unit Title: Chapter 4 Congruent Triangles (cont.) Extension Rotations, reflections, and translations are used to create many works of art. Have students explore using these transformations to create patterns. Students should begin with a single figure in the coordinate plane and use various transformations to turn their figure into an artful pattern. Students should record each pattern used so that the design can be repeated. Resources: Essential Materials, Supplementary Materials, Links to Best Practices, Leveled Worksheets, Personal Tutor, Virtual Manipulatives, 5-Minute Checks, Graphing Calculator Instructional Adjustments: Leveled Worksheets, Differentiation Resources, Scaffolding Questions, Use Watch Out questions provided in the text

20 GEOMETRY HONORS 20 Unit Title: Chapter 5 Relationships in Triangles Targeted Standards: G.CO Prove theorems about triangles and apply geometric methods to solve problems Unit Objectives/Conceptual Understandings: Students will be able to identify and use perpendicular bisectors, angle bisectors, medians and altitudes in triangles, and recognize and apply properties of inequalities to angles and sides of triangles. Essential Questions: What information do we get from knowing that a segment is a median, altitude or angle bisector of a triangle? What inequalities apply to the relationships of angles and sides in triangles? Unit : Teacher-generated assessments will be used. G.CO.10 Prove theorems about triangles G.MG.3 Apply geometric methods to solve problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios) Unit vocabulary including: a. perpendicular bisector b. point of concurrency c. circumcenter d. incenter e. median f. centroid g. altitude h. orthocenter Exterior Angle Inequality Angle-Side Inequalities Construct viable arguments Use perpendicular bisectors in triangles Use angle bisectors in triangles Use medians in triangles Use altitudes in triangles Write indirect proofs Use Real-World Example 2 on Pg 326 to connect the Circumcenter Theorem to reallife problems Use Interior Design Example on Pg 347 to connect Angle-Side Relationships to the real world Use the Cabri Jr. application on a TI-83/84 Plus graphing calculator to discover properties of triangles as outlined on Pg 363 Suggest quizzes after Sec 5.2 and 5.5 Use Exit Ticket included in Sec 5.2 Selected exercises can be used as Formative s as suggested in the textbook The Triangle Inequality Hinge Theorem Use The Triangle Inequality to identify possible triangles Use the Hinge Theorem to make comparisons in two triangles

21 GEOMETRY HONORS 21 Unit Title: Chapter 5 Relationships in Triangles (cont.) Resources: Leveled Worksheets, Personal Tutor, Virtual Manipulatives, 5-Minute Checks Use graphing calculator Teaching Geometry with Manipulatives Instructional Adjustments: Use Leveled Worksheets Use Lesson Resources to provide differentiation Use scaffolding questions provided at the start of each lesson

22 GEOMETRY HONORS 22 Unit Title: Chapter 6 Quadrilaterals Targeted Standards: G.CO and G.MG Prove theorems about parallelograms, apply geometric methods to solve problems, use coordinates to prove geometric theorems Unit Objectives/Conceptual Understandings: Students will recognize properties of quadrilaterals that determine the most descriptive quadrilateral and apply properties of polygons to solve problems Essential Questions: What properties determine a parallelogram and/or special parallelograms? Unit : Teacher-generated assessments will be used G.MG.1 Use geometric shapes, their measures and their properties to describe objects G.CO.11 Prove theorems about parallelograms G.GPE.4 Use coordinates to prove simple geometric theorems algebraically G.MG.3 Apply geometric methods to solve problems Unit Vocabulary including: a. diagonal b. parallelogram c. rectangle d. rhombus e. square f. trapezoid g. bases h. legs of a trapezoid i. base angles j. isosceles trapezoid k. midsegment of a trapezoid l. kite Verify that a quadrilateral is a parallelogram Prove that a set of points forms a parallelogram in the coordinate plane Determine whether a parallelogram or a quadrilateral is a rectangle, square or rhombus Apply properties of kites and trapezoids Consider using the Graphing Technology Lab on Pg 412 Assign the Modeling problem (#32) on Pg 427 Consider giving quizzes after Section 6.1, 6.3 and 6.6 Selected exercises can be used as Formative s as suggested in the textbook Properties of: a. parallelogram b. rectangle c. rhombus d. square e. trapezoid

23 GEOMETRY HONORS 23 Unit Title: Chapter 6 Quadrilaterals (cont.) f. isosceles trapezoid g. kite How to find the sum of the measures of the interior and exterior angles of a polygon Resources: Leveled Worksheets, Virtual Manipulatives, Animations, Personal Tutor Graphing calculators Teaching Geometry with Manipulatives Instructional Adjustments: Use Leveled Worksheets Use Lesson Resources to provide differentiation Use scaffolding questions provided at the start of each lesson

24 GEOMETRY HONORS 24 Unit Title: Chapter 7 Proportions and Similarity Targeted Standards: G.SRT Understand similarity, define trigonometric ratios, and apply trigonometry in problem solving. Unit Objectives/Conceptual Understandings: Students will be able to identify similar triangles. Essential Questions: How do we prove that triangles are similar? How can we use proportional relationships in similar triangles to find missing dimensions? Unit : Teacher-generated assessments will be used. G.MG.3 Apply geometric methods to solve problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost, working with typographic grid systems based on ratios) G.SRT.2 Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar, explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides. G.SRT.4 Prove theorems about triangles G.SRT.5 Use congruence and similarity criteria for triangles to Unit vocabulary including: a. ratio b. proportion c. cross products d. similar polygons e. similar ratio f. scale factor g. midsegment of a triangle h. fractal i. iteration j. self-similar k. dilation l. similarity transformation m. scale factor of a dilation n. scale model o. scale drawing p. scale How to identify similar triangles Prove that triangles are similar Use proportional relationships of corresponding segments of similar triangles to solve problems Use scale factors to solve problems. Consider doing the Graphing Technology Lab which relates the Fibonacci Sequence and Ratios (Pg 468) The Geometry Lab on Pg 488 uses similar triangles to prove the slope criteria for perpendicular and parallel lines The Geometry Lab on Pg investigates iteration and fractals Quizzes are suggested after Section 7.2, 7.4 and 7.6 Selected exercises can be used as Formative s as suggested in the textbook

25 GEOMETRY HONORS 25 Unit Title: Chapter 7 Proportions and Similarity (cont.) solve problems and to prove relationships in geometric figures. How to identify similarity transformations Resources: Leveled Worksheets, Virtual Manipulatives, Animations, Personal Tutor Graphing calculators to be used with the Lab on Pg 468 Teaching Geometry with Manipulatives Instructional Adjustments: Use Leveled Worksheets Use Lesson Resources to provide differentiation Use scaffolding questions provided at the start of each lesson

26 GEOMETRY HONORS 26 Unit Title: Chapter 8 Right Triangles and Trigonometry Targeted Standards: G.SRT Solve problems involving right triangles and apply trigonometry to right triangles Unit Objectives/Conceptual Understandings: Students will be able to solve problems involving right triangles, using Pythagorean Theorem, special right triangles, and trigonometric ratios Essential Questions: How do we use the Pythagorean Theorem and trigonometric ratios to solve problems Unit : Teacher-generated assessments will be used. G.SRT.4 Prove theorems about triangles G.SRT.5 Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures G.SRT.6 Understand that by similarity, the side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles. G.SRT.7 Explain and use the relationship between the sine and cosine of complementary angles. G.SRT.8 Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems Unit vocabulary including: a. Geometric mean b. Pythagorean triple c. Trigonometry d. Trigonometric ratio e. Sine f. Cosine g. Tangent h. Inverse sine i. Inverse cosine j. Inverse tangent k. Cosecant l. Secant m. Cotangent n. Angle of elevation o. Angle of depression p. Law of Sines q. Law of Cosines r. Vector s. Magnitude t. Direction u. Standard position v. Component form w. Resultant Find the geometric mean between two numbers Solve problems involving relationships between parts of a right triangle and the altitude to the hypotenuse Solve problems using the Pythagorean Theorem and its Converse Use properties of and triangles to solve problems Find trigonometric ratios using right triangles Use trigonometric ratios to find angle measures in right triangles Solve problems involving angles of elevation and depression Use the Cabri Jr. application on a graphing calculator to explore trigonometry, the study of the patterns in right triangles Make real life connections by solving problems involving playground (Pg #44), sports (Pg #11), roller coasters (Pg #35), and angles of elevation and depression Quizzes are provided in Sections 8-2, 8-4, 8-6, and 8-7. Selected exercises can be used as Formative s as suggested in the textbook Use the Exit Ticket suggested in Lesson 8-5 on Pg 587

27 GEOMETRY HONORS 27 Unit Title: Chapter 8 Right Triangles and Trigonometry (cont.) G.SRT.9 Derive the formula A = ab sin(c) for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side. The Pythagorean Theorem and its Converse Common Pythagorean triples Use the Law of Sines and the Law of Cosines Perform vector operations G.SRT.10 Prove the Laws of Sines and Cosines The side relationships of and triangles G.MG.3 Apply geometric methods to solve problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost, working with typographic grid systems based on ratios). G.GPE.6 - Find the point on a directed line segment between two given points that partitions the segment in a given ratio. Resources: Leveled Worksheets, Virtual Manipulatives, Animations, Personal Tutor Graphing calculators to be used with the Lab on Pg 567 Teaching Geometry with Manipulatives Instructional Adjustments: Use Leveled Worksheets Use Lesson Resources to provide differentiation Use scaffolding questions provided at the start of each lesson

28 GEOMETRY HONORS 28 Unit Title: Chapter 9 Transformations and Symmetry Targeted Standards: G.CO Experiment with transformations in the plane. Understand congruence in terms of rigid motions. Prove geometric theorems. G.MD Explain volume formulas and use them to solve problems. G.SRT Understand similarity in terms of similarity transformations. Unit Objectives/Conceptual Understandings: Students will be able to: Use congruence transformations to make conjectures and justify properties of geometric figures. Essential Questions: Where can transformations be found? Why is symmetry desirable? Unit : Teacher-generated assessments will be used. Progress Indicators G.CO.2 Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch). G.CO.3 Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself. G.CO.4 Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular Unit vocabulary including: a. line of reflection b. center of rotation c. angle of rotation d. composition of transformations e. symmetry f. line symmetry g. line of symmetry Draw a reflection in a line of reflection and in the coordinate plane. Draw translations in a plane and in a coordinate plane. Draw reflections in a line and in a coordinate plane. Draw translations in a plane and in the coordinate plane. Verify reflections and translations as congruence Draw reflections. Draw reflections in the coordinate plane. Draw translations. Draw translations in the coordinate plane. Draw rotations. Draw rotations in the coordinate plane. Explore the effects of performing multiple transformations on a figure. Identify line and rotational symmetries in twodimensional figures. Identify plane and axis symmetries in threedimensional figures. Create three or four large coordinate grids using poster board. Provide several laminated shapes, such as rectangles, hexagons, pentagons, and trapezoids. Students can practice physically translating shapes on the grids. Students can use examples of translations in the lesson or create their own. There are many examples of objects in nature that have symmetry. Have students draw or gather examples of objects in nature for each of the types of symmetry discussed in this lesson. Ask students to list the steps in constructing a dilation. Students should include examples that illustrate the steps and list the Use formative assessments suggested in the textbook. Use Guided Practice, Check Your Understanding, HOT problems, and Spiral Reviews as needed. Use Ticket Out the Door Section 9.1 and 9.6. Use Mid-Chapter Quiz Lesson p 649. Use Self-Check Quizzes as needed.

29 GEOMETRY HONORS 29 Unit Title: Chapter 9 Transformations and Symmetry (cont.) Progress Indicators lines, parallel lines, and line segments. G.CO.5 Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another. transformations. Draw reflections and rotations of figures. Draw dilations. Draw dilations in the coordinate plane. properties of a dilation. G.CO.8 Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions. G.CO.12 Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). G.MD.4 Identify the shapes of two-dimensional crosssections of three-dimensional objects, and identify threedimensional objects generated by rotations of two-

30 GEOMETRY HONORS 30 Unit Title: Chapter 9 Transformations and Symmetry (cont.) Progress Indicators dimensional objects. G.SRT.1 Verify experimentally the properties of dilations given by a center and a scale factor. Resources: Leveled Worksheets, Personal Tutor, Virtual Manipulatives, 5-Minute Checks found on connect.ed.mcgraw-hill.com Geometer Sketchpad Graphing Calculator Teaching Geometry with Manipulatives Instructional Adjustments: Use Leveled Worksheets. Use Lesson Resources to provide differentiation. Use scaffolding questions provided at the start of each lesson. Use error analysis and Watch Out tips suggested in the textbook. Use Tip for New Teachers suggested in the textbook.

31 GEOMETRY HONORS 31 Unit Title: Chapter 10 Circles Targeted Standards: G.CO Experiment with transformations in the plane. G.C Understand and apply theorems about circles. G.MG Apply geometric concepts in modeling situations. G.GPE Translate between the geometric description and the equation for a conic section. Unit Objectives/Conceptual Understandings: Find areas of sectors and arc lengths of circles using proportional reasoning. Use numeric and geometric patterns to make generalizations about geometric properties including properties of angle relationships in circles. Essential Questions: How can circles be used? Unit : Teacher-generated assessments will be used. G.CO.1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc. G.CO.12 Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). G.CO.13 Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle. Unit vocabulary including: a. circle b. center c. radius d. chord e. diameter f. circumference g. pi (π) h. inscribed i. circumscribed j. central angle k. arc l. tangent m. secant n. chord segment Radius-chord relationships Arc-chord-central angle relationships What students will be Identify and use parts of circles. Solve problems involving the circumference of a circle. Identify and measure central angles, arcs, and semicircles. Find arc length. Recognize and use relationships between arcs and chords. Recognize and use relationships between arcs, chords, and diameters. Find measures of Visual/Spatial Learners Instruct students to use a piece of string to estimate the circumference of discs or cylinders. Then have students measure the diameter of the object. Review the formulas for finding circumference by using the diameter and the radius. Have students find the circumference mathematically, using the diameter and then the radius. Have students compare their calculations with the estimate they found by using the string. Verbal/Linguistic Learners Have students construct a circle with two congruent Suggested quiz after section 10.2 Suggested quiz after section 10.4 Suggested quiz after section 10.6 Suggested quiz after section 10.8 Exit tickets provided in text Teacher-generated exit tickets Teacher-generated formative/summative assessment

32 GEOMETRY HONORS 32 Unit Title: Chapter 10 Circles (cont.) G.C.1 Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation. G.C.2 Derive the equation of a parabola given a focus and directrix. G.C.3 Use coordinates to prove simple geometric theorems algebraically. G.C.4 Use coordinates to prove simple geometric theorems algebraically. G.C.5 Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). G.MG.3 Apply geometric methods to solve problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios). Inscribed Angle Theorem Tangent-radius relationships Theorems about angles formed by secants, tangents, and chords Equation of a circle in standard form What students will be inscribed angles. Find measures of angles of inscribed polygons. Use properties of tangents. Solve problems involving circumscribed polygons. Find measures of angles formed by lines intersecting on or inside a circle. Find measures of angles formed by lines intersecting outside a circle. Find measures of segments that intersect in the interior of a circle. Find measures of segments that intersect in the exterior of a circle. Write the equation of a circle. Graph a circle on the coordinate plane. chords and the perpendicular bisectors. Then have them write a proof supporting the congruency of their construction. Extension Have students describe the difference between a central angle and an inscribed angle, and how their measures are related if they intercept the same arc. Extension Have each student find another real-life example of segments of circles in construction, nature, and so on. Instruct students to write a brief explanation of the example they found, construct a sketch of the example, insert accurate measurements if possible, and then write an equation on the information.

### Chapter 111. Texas Essential Knowledge and Skills for Mathematics. Subchapter B. Middle School

Middle School 111.B. Chapter 111. Texas Essential Knowledge and Skills for Mathematics Subchapter B. Middle School Statutory Authority: The provisions of this Subchapter B issued under the Texas Education

### Algebra and Geometry Review (61 topics, no due date)

Course Name: Math 112 Credit Exam LA Tech University Course Code: ALEKS Course: Trigonometry Instructor: Course Dates: Course Content: 159 topics Algebra and Geometry Review (61 topics, no due date) Properties

### Functional Math II. Information CourseTitle. Types of Instruction

Functional Math II Course Outcome Summary Riverdale School District Information CourseTitle Functional Math II Credits 0 Contact Hours 135 Instructional Area Middle School Instructional Level 8th Grade

### The Australian Curriculum Mathematics

The Australian Curriculum Mathematics Mathematics ACARA The Australian Curriculum Number Algebra Number place value Fractions decimals Real numbers Foundation Year Year 1 Year 2 Year 3 Year 4 Year 5 Year

### College Prep. Geometry Course Syllabus

College Prep. Geometry Course Syllabus Mr. Chris Noll Turner Ashby High School - Room 211 Email: cnoll@rockingham.k12.va.us Website: http://blogs.rockingham.k12.va.us/cnoll/ School Phone: 828-2008 Text:

### For example, estimate the population of the United States as 3 times 10⁸ and the

CCSS: Mathematics The Number System CCSS: Grade 8 8.NS.A. Know that there are numbers that are not rational, and approximate them by rational numbers. 8.NS.A.1. Understand informally that every number

### Appendix A Designing High School Mathematics Courses Based on the Common Core Standards

Overview: The Common Core State Standards (CCSS) for Mathematics are organized by grade level in Grades K 8. At the high school level, the standards are organized by strand, showing a logical progression

### About Tutorials... 1 Algebra I... 2 Geometry... 3 Algebra II... 4 English I... 5 English II... 6 English III... 7

Outlines Texas Tutorials Apex Learning Texas Tutorials provide teachers with a solution to support all students in rising to the expectations established by the Texas state standards. With content developed

### Such As Statements, Kindergarten Grade 8

Such As Statements, Kindergarten Grade 8 This document contains the such as statements that were included in the review committees final recommendations for revisions to the mathematics Texas Essential

### Further Steps: Geometry Beyond High School. Catherine A. Gorini Maharishi University of Management Fairfield, IA cgorini@mum.edu

Further Steps: Geometry Beyond High School Catherine A. Gorini Maharishi University of Management Fairfield, IA cgorini@mum.edu Geometry the study of shapes, their properties, and the spaces containing

### MATH 0110 Developmental Math Skills Review, 1 Credit, 3 hours lab

MATH 0110 Developmental Math Skills Review, 1 Credit, 3 hours lab MATH 0110 is established to accommodate students desiring non-course based remediation in developmental mathematics. This structure will

### Support Materials for Core Content for Assessment. Mathematics

Support Materials for Core Content for Assessment Version 4.1 Mathematics August 2007 Kentucky Department of Education Introduction to Depth of Knowledge (DOK) - Based on Norman Webb s Model (Karin Hess,

### LAKE ELSINORE UNIFIED SCHOOL DISTRICT

LAKE ELSINORE UNIFIED SCHOOL DISTRICT Title: PLATO Algebra 1-Semester 2 Grade Level: 10-12 Department: Mathematics Credit: 5 Prerequisite: Letter grade of F and/or N/C in Algebra 1, Semester 2 Course Description:

### 04 Mathematics CO-SG-FLD004-03. Program for Licensing Assessments for Colorado Educators

04 Mathematics CO-SG-FLD004-03 Program for Licensing Assessments for Colorado Educators Readers should be advised that this study guide, including many of the excerpts used herein, is protected by federal

### Oklahoma School Testing Program

Oklahoma School Testing Program Oklahoma Core Curriculum Tests (OCCT) End-of-Instruction ACE Geometry Parent, Student, and Teacher Guide Winter/Trimester 013 01 Oklahoma State Department of Education 70561-W

### 12-1 Representations of Three-Dimensional Figures

Connect the dots on the isometric dot paper to represent the edges of the solid. Shade the tops of 12-1 Representations of Three-Dimensional Figures Use isometric dot paper to sketch each prism. 1. triangular

### Extra Credit Assignment Lesson plan. The following assignment is optional and can be completed to receive up to 5 points on a previously taken exam.

Extra Credit Assignment Lesson plan The following assignment is optional and can be completed to receive up to 5 points on a previously taken exam. The extra credit assignment is to create a typed up lesson

### Secondary Mathematics Syllabuses

Secondary Mathematics Syllabuses Copyright 006 Curriculum Planning and Development Division. This publication is not for sale. All rights reserved. No part of this publication may be reproduced without

### Math at a Glance for April

Audience: School Leaders, Regional Teams Math at a Glance for April The Math at a Glance tool has been developed to support school leaders and region teams as they look for evidence of alignment to Common

### Unit 5 Area. What Is Area?

Trainer/Instructor Notes: Area What Is Area? Unit 5 Area What Is Area? Overview: Objective: Participants determine the area of a rectangle by counting the number of square units needed to cover the region.

### Natural Disaster Recovery and Quadrilaterals

Natural Disaster Recovery and Quadrilaterals I. UNIT OVERVIEW & PURPOSE: In this unit, students will apply their knowledge of quadrilaterals to solve mathematics problems concerning a tornado that struck

### GeoGebra. 10 lessons. Gerrit Stols

GeoGebra in 10 lessons Gerrit Stols Acknowledgements GeoGebra is dynamic mathematics open source (free) software for learning and teaching mathematics in schools. It was developed by Markus Hohenwarter

### PHILOSOPHY OF THE MATHEMATICS DEPARTMENT

PHILOSOPHY OF THE MATHEMATICS DEPARTMENT The Lemont High School Mathematics Department believes that students should develop the following characteristics: Understanding of concepts and procedures Building

### Mathematics: Content Knowledge

The Praxis Study Companion Mathematics: Content Knowledge 5161 www.ets.org/praxis Welcome to the Praxis Study Companion Welcome to the Praxis Study Companion Prepare to Show What You Know You have been

### Mathematics (MAT) MAT 061 Basic Euclidean Geometry 3 Hours. MAT 051 Pre-Algebra 4 Hours

MAT 051 Pre-Algebra Mathematics (MAT) MAT 051 is designed as a review of the basic operations of arithmetic and an introduction to algebra. The student must earn a grade of C or in order to enroll in MAT

### 8th Grade Texas Mathematics: Unpacked Content

8th Grade Texas Mathematics: Unpacked Content What is the purpose of this document? To increase student achievement by ensuring educators understand specifically what the new standards mean a student must

### Math Course Descriptions & Student Learning Outcomes

Math Course Descriptions & Student Learning Outcomes Table of Contents MAC 100: Business Math... 1 MAC 101: Technical Math... 3 MA 090: Basic Math... 4 MA 095: Introductory Algebra... 5 MA 098: Intermediate

### Regents Examination in Geometry (Common Core) Sample and Comparison Items Spring 2014

Regents Examination in Geometry (Common Core) Sample and Comparison Items Spring 2014 i May 2014 777777 THE STATE EDUCATION DEPARTMENT / THE UNIVERSITY OF THE STATE OF NEW YORK / ALBANY, NY 12234 New York

### MTH124: Honors Algebra I

MTH124: Honors Algebra I This course prepares students for more advanced courses while they develop algebraic fluency, learn the skills needed to solve equations, and perform manipulations with numbers,

### Algebra I Credit Recovery

Algebra I Credit Recovery COURSE DESCRIPTION: The purpose of this course is to allow the student to gain mastery in working with and evaluating mathematical expressions, equations, graphs, and other topics,

### Florida Math for College Readiness

Core Florida Math for College Readiness Florida Math for College Readiness provides a fourth-year math curriculum focused on developing the mastery of skills identified as critical to postsecondary readiness

### DOE FUNDAMENTALS HANDBOOK MATHEMATICS Volume 2 of 2

DOE-HDBK-1014/2-92 JUNE 1992 DOE FUNDAMENTALS HANDBOOK MATHEMATICS Volume 2 of 2 U.S. Department of Energy Washington, D.C. 20585 FSC-6910 Distribution Statement A. Approved for public release; distribution

### TExMaT I Texas Examinations for Master Teachers. Preparation Manual. 088 Master Mathematics Teacher 4 8

TExMaT I Texas Examinations for Master Teachers Preparation Manual 088 Master Mathematics Teacher 4 8 Copyright 2006 by the Texas Education Agency (TEA). All rights reserved. The Texas Education Agency

### Questions. Strategies August/September Number Theory. What is meant by a number being evenly divisible by another number?

Content Skills Essential August/September Number Theory Identify factors List multiples of whole numbers Classify prime and composite numbers Analyze the rules of divisibility What is meant by a number

### Warning! Construction Zone: Building Solids from Nets

Brief Overview: Warning! Construction Zone: Building Solids from Nets In this unit the students will be examining and defining attributes of solids and their nets. The students will be expected to have

### Polynomial Operations and Factoring

Algebra 1, Quarter 4, Unit 4.1 Polynomial Operations and Factoring Overview Number of instructional days: 15 (1 day = 45 60 minutes) Content to be learned Identify terms, coefficients, and degree of polynomials.

### Performance Assessment Task Which Shape? Grade 3. Common Core State Standards Math - Content Standards

Performance Assessment Task Which Shape? Grade 3 This task challenges a student to use knowledge of geometrical attributes (such as angle size, number of angles, number of sides, and parallel sides) to

### Understanding Basic Calculus

Understanding Basic Calculus S.K. Chung Dedicated to all the people who have helped me in my life. i Preface This book is a revised and expanded version of the lecture notes for Basic Calculus and other

### Algebra 1 Course Information

Course Information Course Description: Students will study patterns, relations, and functions, and focus on the use of mathematical models to understand and analyze quantitative relationships. Through

### Resource Guide to the Arkansas Curriculum Framework for Students with Disabilities for Ninth Grade Mathematics. Summer 2005

Resource Guide to the Arkansas Curriculum Framework for Students with Disabilities for Ninth Grade Mathematics Summer 2005 Purpose and Process The Individuals with Disabilities Education Act and No Child

### COURSE SYLLABUS -----------------------------------------------------------------------------------

Last Reviewed by: Leslie Wurst Date Approved: Date Revised: Fall 2012 COURSE SYLLABUS Syllabus for: MATH 1010 Math for General Studies Former Course and Title: Former Quarter Course(s): Mat 1260 Contemporary

### March 2013 Mathcrnatics MATH 92 College Algebra Kerin Keys. Dcnnis. David Yec' Lscture: 5 we ekly (87.5 total)

City College of San Irrancisco Course Outline of Itecord I. GENERAI- DESCRIPI'ION A. Approval Date B. Departrnent C. Course Number D. Course Title E. Course Outline Preparer(s) March 2013 Mathcrnatics

### Inversion. Chapter 7. 7.1 Constructing The Inverse of a Point: If P is inside the circle of inversion: (See Figure 7.1)

Chapter 7 Inversion Goal: In this chapter we define inversion, give constructions for inverses of points both inside and outside the circle of inversion, and show how inversion could be done using Geometer

### INDIANA ACADEMIC STANDARDS. Mathematics: Grade 6 Draft for release: May 1, 2014

INDIANA ACADEMIC STANDARDS Mathematics: Grade 6 Draft for release: May 1, 2014 I. Introduction The Indiana Academic Standards for Mathematics are the result of a process designed to identify, evaluate,

### Administrative - Master Syllabus COVER SHEET

Administrative - Master Syllabus COVER SHEET Purpose: It is the intention of this to provide a general description of the course, outline the required elements of the course and to lay the foundation for

### 2.5 If-Then Statements and

Page 1 of 6 2.5 If-Then Statements and Deductive Reasoning Goal Use if-then statements. Apply laws of logic. An if-then statement has two parts. The if part contains the hypothesis. The then part contains

### A Review of Four High-School Mathematics Programs. Guershon Harel University of California, San Diego harel@math.ucsd.edu

1 A Review of Four High-School Mathematics Programs Guershon Harel University of California, San Diego harel@math.ucsd.edu 1. Introduction Recently I was commissioned by Strategic Teaching to review four

### Graphing and Solving Nonlinear Inequalities

APPENDIX LESSON 1 Graphing and Solving Nonlinear Inequalities New Concepts A quadratic inequality in two variables can be written in four different forms y < a + b + c y a + b + c y > a + b + c y a + b

### Mathematics. Mathematics MATHEMATICS. 298 2015-16 Sacramento City College Catalog. Degree: A.S. Mathematics AS-T Mathematics for Transfer

MATH Degree: A.S. AS-T for Transfer Division of /Statistics & Engineering Anne E. Licciardi, Dean South Gym 220 916-558-2202 Associate in Science Degree Program Information The mathematics program provides

### NOT AN OFFICIAL SCORE REPORT. Summary of Results

From SAT TEST MARCH 8, 214 Summary of Results Page 1 of 1 Congratulations on taking the SAT Reasoning Test! You re showing colleges that you are serious about getting an education. The SAT is one indicator

### Determine whether the following lines intersect, are parallel, or skew. L 1 : x = 6t y = 1 + 9t z = 3t. x = 1 + 2s y = 4 3s z = s

Homework Solutions 5/20 10.5.17 Determine whether the following lines intersect, are parallel, or skew. L 1 : L 2 : x = 6t y = 1 + 9t z = 3t x = 1 + 2s y = 4 3s z = s A vector parallel to L 1 is 6, 9,

### TExMaT I Texas Examinations for Master Teachers. Preparation Manual. 087 Master Mathematics Teacher EC 4

TExMaT I Texas Examinations for Master Teachers Preparation Manual 087 Master Mathematics Teacher EC 4 Copyright 2006 by the Texas Education Agency (TEA). All rights reserved. The Texas Education Agency

### A Second Course in Mathematics Concepts for Elementary Teachers: Theory, Problems, and Solutions

A Second Course in Mathematics Concepts for Elementary Teachers: Theory, Problems, and Solutions Marcel B. Finan Arkansas Tech University c All Rights Reserved First Draft February 8, 2006 1 Contents 25

### TExES Texas Examinations of Educator Standards. Preparation Manual. 135 Mathematics 8 12

TExES Texas Examinations of Educator Standards Preparation Manual 135 Mathematics 8 1 Copyright 010 by Texas Education Agency (TEA). All rights reserved. The Texas Education Agency logo and TEA are registered

### Content. Chapter 4 Functions 61 4.1 Basic concepts on real functions 62. Credits 11

Content Credits 11 Chapter 1 Arithmetic Refresher 13 1.1 Algebra 14 Real Numbers 14 Real Polynomials 19 1.2 Equations in one variable 21 Linear Equations 21 Quadratic Equations 22 1.3 Exercises 28 Chapter

### Course Outlines. 1. Name of the Course: Algebra I (Standard, College Prep, Honors) Course Description: ALGEBRA I STANDARD (1 Credit)

Course Outlines 1. Name of the Course: Algebra I (Standard, College Prep, Honors) Course Description: ALGEBRA I STANDARD (1 Credit) This course will cover Algebra I concepts such as algebra as a language,

### Maryland English Language Arts

Maryland English Language Arts A S O F J U N E 2 0, 2 0 1 0, T H I S S TAT E H A D A D O P T E D T H E CO M M O N CO R E S TAT E S TA N DA R D S. DOCUMENTS REVIEWED Maryland Voluntary State Curriculum:

### SAN DIEGO COMMUNITY COLLEGE DISTRICT CITY COLLEGE ASSOCIATE DEGREE COURSE OUTLINE

MATH 098 CIC Approval: BOT APPROVAL: STATE APPROVAL: EFFECTIVE TERM: SAN DIEGO COMMUNITY COLLEGE DISTRICT CITY COLLEGE ASSOCIATE DEGREE COURSE OUTLINE SECTION I SUBJECT AREA AND COURSE NUMBER: Mathematics

### Section 1.1. Introduction to R n

The Calculus of Functions of Several Variables Section. Introduction to R n Calculus is the study of functional relationships and how related quantities change with each other. In your first exposure to

### Objectives After completing this section, you should be able to:

Chapter 5 Section 1 Lesson Angle Measure Objectives After completing this section, you should be able to: Use the most common conventions to position and measure angles on the plane. Demonstrate an understanding

### Mathematics. Designing High School Mathematics Courses Based on the Common

common core state STANDARDS FOR Mathematics Appendix A: Designing High School Mathematics Courses Based on the Common Core State Standards Overview The (CCSS) for Mathematics are organized by grade level

### Algebra Unpacked Content For the new Common Core standards that will be effective in all North Carolina schools in the 2012-13 school year.

This document is designed to help North Carolina educators teach the Common Core (Standard Course of Study). NCDPI staff are continually updating and improving these tools to better serve teachers. Algebra

### http://school-maths.com Gerrit Stols

For more info and downloads go to: http://school-maths.com Gerrit Stols Acknowledgements GeoGebra is dynamic mathematics open source (free) software for learning and teaching mathematics in schools. It

### CHAPTER 1. LINES AND PLANES IN SPACE

CHAPTER 1. LINES AND PLANES IN SPACE 1. Angles and distances between skew lines 1.1. Given cube ABCDA 1 B 1 C 1 D 1 with side a. Find the angle and the distance between lines A 1 B and AC 1. 1.2. Given

### Middle School Mathematics

The Praxis Study Companion Middle School Mathematics 5169 www.ets.org/praxis Welcome to the Praxis Study Companion Welcome to The Praxis Study Companion Prepare to Show What You Know You have been working

### Possible Stage Two Mathematics Test Topics

Possible Stage Two Mathematics Test Topics The Stage Two Mathematics Test questions are designed to be answerable by a good problem-solver with a strong mathematics background. It is based mainly on material

### -!4(%-!4)#3 (IGH 3CHOOL #ONTENT %XPECTATIONS. Quantitative Literacy and Logic. Algebra and Functions. Geometry and Trigonometry

(IGH 3CHOOL #ONTENT %XPECTATIONS -!4(%-!4)#3 n Quantitative Literacy and Logic n Algebra and Functions n Geometry and Trigonometry n Statistics and Probability 11/07 Mathematics Work Group Michigan State

### Algebra II and Trigonometry

Algebra II and Trigonometry Textbooks: Algebra 2: California Publisher: McDougal Li@ell/Houghton Mifflin (2006 EdiHon) ISBN- 13: 978-0618811816 Course descriphon: Algebra II complements and expands the

### What to Expect on the Compass

What to Expect on the Compass What is the Compass? COMPASS is a set of untimed computer adaptive tests created by the American College Test (ACT) Program. Because COMPASS tests are "computer adaptive,"

### MATH APPLICATIONS CURRICULUM

MATH APPLICATIONS CURRICULUM NEWTOWN SCHOOLS NEWTOWN, CT. August, 1997 MATHEMATICS PHILOSOPHY We believe mathematics instruction should develop students' ability to solve problems. We believe that the

### Curriculum Overview Standards & Skills

Curriculum Overview Standards & Skills You CAN Do The Rubik's Cube Instructional Curriculum Curriculum Overview / Skills & Standards How to Solve The Rubik's Cube Part 1 - Curriculum Overview Part 2 -

### 13. Write the decimal approximation of 9,000,001 9,000,000, rounded to three significant

æ If 3 + 4 = x, then x = 2 gold bar is a rectangular solid measuring 2 3 4 It is melted down, and three equal cubes are constructed from this gold What is the length of a side of each cube? 3 What is the

### MATHEMATICS & STATISTICS

Area: Mathematics Dean: Nancy Reitz, Interim Phone: (916) 484-8215 Counseling: (916) 484-8572 Mathematics Degree The A.S. degree in mathematics provides a foundation of mathematics for students in preparation

### Kindergarten to Grade 3. Geometry and Spatial Sense

Kindergarten to Grade 3 Geometry and Spatial Sense Every effort has been made in this publication to identify mathematics resources and tools (e.g., manipulatives) in generic terms. In cases where a particular

### Stephanie A. Mungle TEACHING PHILOSOPHY STATEMENT

Stephanie A. Mungle TEACHING PHILOSOPHY STATEMENT I am a self-directed, enthusiastic college mathematics educator with a strong commitment to student learning and excellence in teaching. I bring my passion

### Prerequisites: TSI Math Complete and high school Algebra II and geometry or MATH 0303.

Course Syllabus Math 1314 College Algebra Revision Date: 8-21-15 Catalog Description: In-depth study and applications of polynomial, rational, radical, exponential and logarithmic functions, and systems

### COLLEGE ALGEBRA LEARNING COMMUNITY

COLLEGE ALGEBRA LEARNING COMMUNITY Tulsa Community College, West Campus Presenter Lori Mayberry, B.S., M.S. Associate Professor of Mathematics and Physics lmayberr@tulsacc.edu NACEP National Conference

### College Algebra. Barnett, Raymond A., Michael R. Ziegler, and Karl E. Byleen. College Algebra, 8th edition, McGraw-Hill, 2008, ISBN: 978-0-07-286738-1

College Algebra Course Text Barnett, Raymond A., Michael R. Ziegler, and Karl E. Byleen. College Algebra, 8th edition, McGraw-Hill, 2008, ISBN: 978-0-07-286738-1 Course Description This course provides

### SINUS. international. Towards New Teaching in Mathematics. Dynamic Geometry with Polygon Pantographs 8. Wolfgang Neidhardt 8 / 2011.

SINUS international Towards New Teaching in Mathematics Wolfgang Neidhardt Dynamic Geometry with Polygon Pantographs 8 Peter Baptist Carsten Miller 8 / 2011 ISSN 2192-7596 Dagmar Raab University of Bayreuth

College Readiness Math MOOC Instructor Information: Dr. Jennifer Kosiak, jkosiak@uwlax.edu General email: mathmooc@uwlax.edu Mathematics Department, University of Wisconsin- La Crosse Description: The

### Blue Pelican Alg II First Semester

Blue Pelican Alg II First Semester Teacher Version 1.01 Copyright 2009 by Charles E. Cook; Refugio, Tx (All rights reserved) Alg II Syllabus (First Semester) Unit 1: Solving linear equations and inequalities

### Mathematics as Reasoning Students will use reasoning skills to determine the best method for maximizing area.

Title: A Pen for Penny Brief Overview: This unit is a reinforcement of the concepts of area and perimeter of rectangles. Methods for maximizing area while perimeter remains the same are also included.

### -- Martensdale-St. Marys Community School Math Curriculum

-- Martensdale-St. Marys Community School Standard 1: Students can understand and apply a variety of math concepts. Benchmark; The student will: A. Understand and apply number properties and operations.

Introduction to Quadratic Functions The St. Louis Gateway Arch was constructed from 1963 to 1965. It cost 13 million dollars to build..1 Up and Down or Down and Up Exploring Quadratic Functions...617.2

### Æ Please note that we are continuing to make adjustments to our program to

Degree/Certificate: Bachelor of Arts in Education Major/Option: Mathematics/Elementary and Middle Level Mathematics Endorsement Option Submitted by: Mathematics Education Committee Date: November 1, 2013

### Grade 1. M3: Ordering and Expressing Length Measurements as Numbers

Grade 1 Key Areas of Focus for Grades K-2: Addition and subtraction-concepts, skills and problem solving Expected Fluency: Add and Subtract within 10 Module M1: Addition and Subtraction of Numbers to 10

### DRAFT. New York State Testing Program Grade 8 Common Core Mathematics Test. Released Questions with Annotations

DRAFT New York State Testing Program Grade 8 Common Core Mathematics Test Released Questions with Annotations August 2014 Developed and published under contract with the New York State Education Department

### Diablo Valley College Catalog 2014-2015

Mathematics MATH Michael Norris, Interim Dean Math and Computer Science Division Math Building, Room 267 Possible career opportunities Mathematicians work in a variety of fields, among them statistics,

### Connections Across Strands Provides a sampling of connections that can be made across strands, using the theme (integers) as an organizer.

Overview Context Connections Positions integers in a larger context and shows connections to everyday situations, careers, and tasks. Identifies relevant manipulatives, technology, and web-based resources

### David Bressoud Macalester College, St. Paul, MN. NCTM Annual Mee,ng Washington, DC April 23, 2009

David Bressoud Macalester College, St. Paul, MN These slides are available at www.macalester.edu/~bressoud/talks NCTM Annual Mee,ng Washington, DC April 23, 2009 The task of the educator is to make the

### South Carolina College- and Career-Ready Standards for Mathematics

South Carolina College- and Career-Ready Standards for Mathematics South Carolina Department of Education Columbia, South Carolina 2015 State Board of Education Approved First Reading on February 11, 2015

### 2009 Chicago Area All-Star Math Team Tryouts Solutions

1. 2009 Chicago Area All-Star Math Team Tryouts Solutions If a car sells for q 1000 and the salesman earns q% = q/100, he earns 10q 2. He earns an additional 100 per car, and he sells p cars, so his total

### YOU CAN COUNT ON NUMBER LINES

Key Idea 2 Number and Numeration: Students use number sense and numeration to develop an understanding of multiple uses of numbers in the real world, the use of numbers to communicate mathematically, and

### Exemplar Mathematics Test Questions. Computer-Based Tests. discoveractaspire.org

Exemplar Mathematics Test Questions Computer-Based Tests discoveractaspire.org We invite educators, administrators, and policymakers to learn about ACT Aspire by viewing the collection of sample computer-based

### Balanced Assessment Test Algebra 2008

Balanced Assessment Test Algebra 2008 Core Idea Task Score Representations Expressions This task asks students find algebraic expressions for area and perimeter of parallelograms and trapezoids. Successful

### In this section, you will develop a method to change a quadratic equation written as a sum into its product form (also called its factored form).

CHAPTER 8 In Chapter 4, you used a web to organize the connections you found between each of the different representations of lines. These connections enabled you to use any representation (such as a graph,

XV. Mathematics, Grade 10 Grade 10 Mathematics Test The spring 2011 grade 10 MCAS Mathematics test was based on learning standards in the Massachusetts Mathematics Curriculum Framework (2000). The Framework

### Wallingford Public Schools - HIGH SCHOOL COURSE OUTLINE

Wallingford Public Schools - HIGH SCHOOL COURSE OUTLINE Course Title: Computer Aided Drafting & Design Course Number: 7163 Department: Career and Technical Education Grade(s): 9-12 Level(s): Academic Credit: